Summary

Testing the effect of deviance on similarity-based structure and certainty.

Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.

Method changes:

  • 6 agents, 12 issues

  • introductory instructions prompt amended with “… complete a group impressions task…” and “… try to see if you can figure out to what extent each person agrees with everyone else in the group.”

  • PNS scale added

Note: data for prediction values are corrected in R script due to coding error

Demographics (Attention Check)
0
(N=54)
0.25
(N=48)
0.5
(N=59)
0.75
(N=50)
1
(N=67)
Overall
(N=278)
age
Mean (SD) 37.2 (15.3) 35.5 (14.3) 35.7 (14.9) 36.6 (14.0) 36.9 (13.7) 36.4 (14.4)
Median [Min, Max] 35.5 [19.0, 73.0] 32.0 [19.0, 73.0] 31.0 [18.0, 78.0] 33.0 [18.0, 69.0] 34.0 [19.0, 73.0] 33.5 [18.0, 78.0]
race
American Indian or Alaska Native 1 (1.9%) 1 (2.1%) 0 (0%) 0 (0%) 0 (0%) 2 (0.7%)
Asian 5 (9.3%) 7 (14.6%) 6 (10.2%) 6 (12.0%) 6 (9.0%) 30 (10.8%)
Black or African-American 3 (5.6%) 4 (8.3%) 6 (10.2%) 3 (6.0%) 10 (14.9%) 26 (9.4%)
Hispanic/Latinx 1 (1.9%) 0 (0%) 4 (6.8%) 1 (2.0%) 5 (7.5%) 11 (4.0%)
White 44 (81.5%) 35 (72.9%) 43 (72.9%) 40 (80.0%) 46 (68.7%) 208 (74.8%)
Other 0 (0%) 1 (2.1%) 0 (0%) 0 (0%) 0 (0%) 1 (0.4%)
gender
Man 29 (53.7%) 18 (37.5%) 33 (55.9%) 24 (48.0%) 30 (44.8%) 134 (48.2%)
Woman 25 (46.3%) 29 (60.4%) 24 (40.7%) 24 (48.0%) 34 (50.7%) 136 (48.9%)
Non-binary 0 (0%) 1 (2.1%) 1 (1.7%) 1 (2.0%) 3 (4.5%) 6 (2.2%)
Prefer not to answer 0 (0%) 0 (0%) 1 (1.7%) 1 (2.0%) 0 (0%) 2 (0.7%)
0
(N=8)
0.25
(N=1)
0.5
(N=5)
0.75
(N=5)
1
(N=3)
Overall
(N=22)
age
Mean (SD) 51.3 (14.9) 22.0 (NA) 35.6 (17.5) 53.4 (14.7) 45.0 (14.9) 46.0 (16.5)
Median [Min, Max] 50.0 [35.0, 69.0] 22.0 [22.0, 22.0] 27.0 [21.0, 57.0] 62.0 [35.0, 66.0] 51.0 [28.0, 56.0] 50.0 [21.0, 69.0]
race
Asian 1 (12.5%) 0 (0%) 1 (20.0%) 0 (0%) 0 (0%) 2 (9.1%)
White 7 (87.5%) 1 (100%) 1 (20.0%) 5 (100%) 2 (66.7%) 16 (72.7%)
Black or African-American 0 (0%) 0 (0%) 2 (40.0%) 0 (0%) 0 (0%) 2 (9.1%)
Hispanic/Latinx 0 (0%) 0 (0%) 1 (20.0%) 0 (0%) 0 (0%) 1 (4.5%)
American Indian or Alaska Native 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (33.3%) 1 (4.5%)
gender
Man 2 (25.0%) 0 (0%) 1 (20.0%) 3 (60.0%) 1 (33.3%) 7 (31.8%)
Woman 6 (75.0%) 1 (100%) 4 (80.0%) 2 (40.0%) 2 (66.7%) 15 (68.2%)
Agent Learning Plots
NonDeviant Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                   Chisq Df Pr(>Chisq)    
opinion_round                   220.9743  1  < 2.2e-16 ***
Deviant_threshold                51.3731  4  1.865e-10 ***
opinion_round:Deviant_threshold   4.7015  4     0.3193    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend      SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall               0.119 0.00799 Inf     0.103     0.134  14.873  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold emmean     SE  df asymp.LCL asymp.UCL z.ratio p.value
 0                  1.602 0.0994 Inf     1.407     1.797  16.111  <.0001
 0.25               1.012 0.1014 Inf     0.814     1.211   9.980  <.0001
 0.5                0.786 0.0906 Inf     0.608     0.963   8.674  <.0001
 0.75               0.849 0.0983 Inf     0.657     1.042   8.641  <.0001
 1                  0.766 0.0851 Inf     0.600     0.933   9.009  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df asymp.LCL
 Deviant_threshold0 - Deviant_threshold0.25      0.5896 0.142 Inf     0.203
 Deviant_threshold0 - Deviant_threshold0.5       0.8166 0.134 Inf     0.450
 Deviant_threshold0 - Deviant_threshold0.75      0.7527 0.140 Inf     0.372
 Deviant_threshold0 - Deviant_threshold1         0.8358 0.131 Inf     0.480
 Deviant_threshold0.25 - Deviant_threshold0.5    0.2270 0.136 Inf    -0.144
 Deviant_threshold0.25 - Deviant_threshold0.75   0.1631 0.141 Inf    -0.222
 Deviant_threshold0.25 - Deviant_threshold1      0.2462 0.132 Inf    -0.114
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.0639 0.134 Inf    -0.428
 Deviant_threshold0.5 - Deviant_threshold1       0.0193 0.124 Inf    -0.319
 Deviant_threshold0.75 - Deviant_threshold1      0.0831 0.130 Inf    -0.271
 asymp.UCL z.ratio p.value
     0.976   4.159  0.0003
     1.183   6.081  <.0001
     1.134   5.390  <.0001
     1.192   6.402  <.0001
     0.598   1.671  0.4522
     0.548   1.155  0.7767
     0.607   1.863  0.3378
     0.300  -0.478  0.9893
     0.358   0.155  0.9999
     0.437   0.640  0.9685

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Similarity Plot
Similarity Analysis
Type III Analysis of Variance Table with Satterthwaite's method
                             Sum Sq Mean Sq NumDF DenDF F value Pr(>F)    
targetpair                      103     103     1   278   0.406 0.5245    
Deviant_threshold             71505   71505     1   278 282.971 <2e-16 ***
targetpair:Deviant_threshold  32839   32839     1   278 129.955 <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emtrends
 targetpair Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 DN                           -60.1 3.22 278    -66.4   -53.73 -18.650  <.0001
 NN                           -11.7 2.78 278    -17.2    -6.24  -4.212  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 

$contrasts
 contrast estimate   SE  df lower.CL upper.CL t.ratio p.value
 DN - NN     -48.4 4.24 278    -56.7      -40 -11.400  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df  Sum Sq Mean Sq F value   Pr(>F)    
Deviant_threshold   4  35.273  8.8183  15.948 9.56e-12 ***
Residuals         273 150.955  0.5529                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean     SE  df lower.CL upper.CL t.ratio p.value
 0                   1.72 0.1012 273     1.52     1.92  17.002  <.0001
 0.25                1.75 0.1073 273     1.54     1.96  16.316  <.0001
 0.5                 1.88 0.0968 273     1.69     2.07  19.414  <.0001
 0.75                2.33 0.1052 273     2.12     2.54  22.147  <.0001
 1                   2.59 0.0908 273     2.41     2.77  28.543  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df lower.CL
 Deviant_threshold0 - Deviant_threshold0.25     -0.0307 0.148 273   -0.436
 Deviant_threshold0 - Deviant_threshold0.5      -0.1590 0.140 273   -0.544
 Deviant_threshold0 - Deviant_threshold0.75     -0.6085 0.146 273   -1.009
 Deviant_threshold0 - Deviant_threshold1        -0.8725 0.136 273   -1.246
 Deviant_threshold0.25 - Deviant_threshold0.5   -0.1283 0.145 273   -0.525
 Deviant_threshold0.25 - Deviant_threshold0.75  -0.5778 0.150 273   -0.990
 Deviant_threshold0.25 - Deviant_threshold1     -0.8418 0.141 273   -1.228
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.4495 0.143 273   -0.842
 Deviant_threshold0.5 - Deviant_threshold1      -0.7135 0.133 273   -1.078
 Deviant_threshold0.75 - Deviant_threshold1     -0.2640 0.139 273   -0.646
 upper.CL t.ratio p.value
    0.374  -0.208  0.9996
    0.226  -1.135  0.7876
   -0.208  -4.169  0.0004
   -0.499  -6.416  <.0001
    0.269  -0.888  0.9012
   -0.165  -3.845  0.0014
   -0.456  -5.987  <.0001
   -0.057  -3.145  0.0157
   -0.349  -5.374  <.0001
    0.118  -1.900  0.3198

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
 Deviant_threshold emmean     SE  df null t.ratio p.value
 0                   1.72 0.1012 273    2  -2.762  0.0031
 0.25                1.75 0.1073 273    2  -2.319  0.0106
 0.5                 1.88 0.0968 273    2  -1.245  0.1071
 0.75                2.33 0.1052 273    2   3.128  0.9990
 1                   2.59 0.0908 273    2   6.527  1.0000

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 × 13
  model    term              estimate std.error statistic p.value conf.low
  <chr>    <chr>                <dbl>     <dbl>     <dbl>   <dbl>    <dbl>
1 below_.5 Deviant_threshold   -26.2       10.5    -2.50   0.0135    -47.0
2 above_.5 Deviant_threshold    -3.41      10.3    -0.330  0.742     -23.8
  conf.high r.squared adj.r.squared    df df.residual  nobs
      <dbl>     <dbl>         <dbl> <dbl>       <int> <int>
1     -5.49  0.0378         0.0317      1         159   161
2     17.0   0.000627      -0.00512     1         174   176
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value  Pr(>F)  
deviance    4   7630 1907.59  2.3537 0.05425 .
Residuals 273 221253  810.45                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0          60.4 3.87 273     52.8     68.1  15.598  <.0001
 0.25       52.6 4.11 273     44.5     60.7  12.797  <.0001
 0.5        47.3 3.71 273     40.0     54.6  12.754  <.0001
 0.75       52.3 4.03 273     44.4     60.2  12.995  <.0001
 1          45.8 3.48 273     38.9     52.6  13.162  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0 - deviance0.25       7.843 5.65 273   -7.666    23.35   1.389
 deviance0 - deviance0.5       13.155 5.36 273   -1.568    27.88   2.454
 deviance0 - deviance0.75       8.106 5.59 273   -7.237    23.45   1.451
 deviance0 - deviance1         14.650 5.21 273    0.353    28.95   2.814
 deviance0.25 - deviance0.5     5.312 5.53 273   -9.884    20.51   0.960
 deviance0.25 - deviance0.75    0.263 5.75 273  -15.534    16.06   0.046
 deviance0.25 - deviance1       6.807 5.38 273   -7.976    21.59   1.264
 deviance0.5 - deviance0.75    -5.049 5.47 273  -20.076     9.98  -0.923
 deviance0.5 - deviance1        1.495 5.08 273  -12.462    15.45   0.294
 deviance0.75 - deviance1       6.544 5.32 273   -8.066    21.15   1.230
 p.value
  0.6354
  0.1045
  0.5954
  0.0416
  0.8727
  1.0000
  0.7132
  0.8880
  0.9984
  0.7339

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Moderator: Last Opinion
0
(N=54)
0.25
(N=48)
0.5
(N=59)
0.75
(N=50)
1
(N=67)
Overall
(N=278)
pred_maj
Yes 47 (87.0%) 43 (89.6%) 45 (76.3%) 43 (86.0%) 47 (70.1%) 225 (80.9%)
No 7 (13.0%) 5 (10.4%) 14 (23.7%) 7 (14.0%) 18 (26.9%) 51 (18.3%)
Missing 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (3.0%) 2 (0.7%)
# A tibble: 4 × 14
# Groups:   pred_maj [2]
  pred_maj id       term              estimate std.error statistic p.value
  <lgl>    <chr>    <chr>                <dbl>     <dbl>     <dbl>   <dbl>
1 FALSE    below_.5 Deviant_threshold    -19.7      24.8    -0.796  0.434 
2 FALSE    above_.5 Deviant_threshold     43.3      19.1     2.27   0.0294
3 TRUE     below_.5 Deviant_threshold    -21.3      11.1    -1.92   0.0571
4 TRUE     above_.5 Deviant_threshold    -16.5      11.8    -1.40   0.163 
  conf.low conf.high r.squared adj.r.squared    df df.residual  nobs
     <dbl>     <dbl>     <dbl>         <dbl> <dbl>       <int> <int>
1   -70.9     31.4      0.0257      -0.0149      1          24    26
2     4.59    82.0      0.122        0.0982      1          37    39
3   -43.2      0.651    0.0269       0.0196      1         133   135
4   -39.9      6.78     0.0146       0.00716     1         133   135
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value    Pr(>F)    
deviance            4   7282  1820.6  2.3898 0.0512800 .  
pred_maj            1  10112 10112.2 13.2737 0.0003235 ***
deviance:pred_maj   4   7652  1912.9  2.5110 0.0422214 *  
Residuals         266 202645   761.8                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
0
(N=54)
0.25
(N=48)
0.5
(N=59)
0.75
(N=50)
1
(N=67)
Overall
(N=278)
pns_med
High 30 (55.6%) 20 (41.7%) 19 (32.2%) 22 (44.0%) 29 (43.3%) 120 (43.2%)
Low 24 (44.4%) 28 (58.3%) 40 (67.8%) 28 (56.0%) 38 (56.7%) 158 (56.8%)
# A tibble: 4 × 14
# Groups:   pns_med [2]
  pns_med id       term              estimate std.error statistic p.value
  <chr>   <chr>    <chr>                <dbl>     <dbl>     <dbl>   <dbl>
1 High    below_.5 Deviant_threshold   -42.5       14.9    -2.86  0.00567
2 High    above_.5 Deviant_threshold     9.33      16.2     0.577 0.566  
3 Low     below_.5 Deviant_threshold    -6.71      14.8    -0.454 0.651  
4 Low     above_.5 Deviant_threshold   -14.7       13.2    -1.11  0.268  
  conf.low conf.high r.squared adj.r.squared    df df.residual  nobs
     <dbl>     <dbl>     <dbl>         <dbl> <dbl>       <int> <int>
1    -72.2     -12.8   0.109         0.0954      1          67    69
2    -22.9      41.6   0.00487      -0.00977     1          68    70
3    -36.1      22.6   0.00229      -0.00880     1          90    92
4    -40.8      11.5   0.0118        0.00226     1         104   106
Analysis of Variance Table

Response: confidence
                  Df Sum Sq Mean Sq F value   Pr(>F)   
deviance           4   7630  1907.6  2.4332 0.047819 * 
pns_med            1   8280  8279.7 10.5609 0.001303 **
deviance:pns_med   4   2863   715.8  0.9130 0.456789   
Residuals        268 210110   784.0                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Order of deviant across rounds
Opinion Round
0
(N=278)
1
(N=278)
2
(N=278)
3
(N=278)
4
(N=278)
5
(N=278)
6
(N=278)
7
(N=278)
8
(N=278)
9
(N=278)
10
(N=278)
11
(N=278)
Overall
(N=3336)
trialnum
0 47 (16.9%) 44 (15.8%) 46 (16.5%) 59 (21.2%) 37 (13.3%) 48 (17.3%) 39 (14.0%) 38 (13.7%) 40 (14.4%) 40 (14.4%) 54 (19.4%) 49 (17.6%) 541 (16.2%)
1 46 (16.5%) 42 (15.1%) 50 (18.0%) 41 (14.7%) 51 (18.3%) 38 (13.7%) 41 (14.7%) 58 (20.9%) 41 (14.7%) 41 (14.7%) 37 (13.3%) 50 (18.0%) 536 (16.1%)
2 56 (20.1%) 51 (18.3%) 44 (15.8%) 50 (18.0%) 45 (16.2%) 53 (19.1%) 40 (14.4%) 40 (14.4%) 56 (20.1%) 43 (15.5%) 44 (15.8%) 54 (19.4%) 576 (17.3%)
3 34 (12.2%) 37 (13.3%) 43 (15.5%) 42 (15.1%) 50 (18.0%) 50 (18.0%) 50 (18.0%) 40 (14.4%) 46 (16.5%) 33 (11.9%) 44 (15.8%) 33 (11.9%) 502 (15.0%)
4 50 (18.0%) 55 (19.8%) 57 (20.5%) 38 (13.7%) 56 (20.1%) 51 (18.3%) 59 (21.2%) 54 (19.4%) 43 (15.5%) 58 (20.9%) 48 (17.3%) 36 (12.9%) 605 (18.1%)
5 45 (16.2%) 49 (17.6%) 38 (13.7%) 48 (17.3%) 39 (14.0%) 38 (13.7%) 49 (17.6%) 48 (17.3%) 52 (18.7%) 63 (22.7%) 51 (18.3%) 56 (20.1%) 576 (17.3%)
Things to note
  • The PNS moderator is a median split
Unresolved
  • The last opinion moderator is barely significant and none really show the U shape